6.6 Laminate Moduli

The Laminate Moduli are the elastic constants (moduli and Poisson’s ratio) of an equivalent orthotropic material.
\includegraphics[]{./Images/LaminateModuli.png}

Since an orthotropic material cannot represent a laminate exactly, there are two approximations: in-plane moduli and bending moduli. One is better when the loading is primarily membrane (in-plane). The other is better when the loading is primarily flexural (bending). CADEC provides indicators of the quality of the approximation. The closer they are to zero, the better is the quality of the orthotropic approximation.

For in-plane loading, $r_ N$, measures the residual shear-extension coupling, illustrated below,
\includegraphics[]{./Images/Fig67d.png}

which would not happen in a (perfect) orthotropic material.

In a $[55/-55]$ laminate, the 55 balances the -55, so we do not get this effect, i.e., $\gamma _{xy}^0=0$, as shown in Figure 6.2.

Also for in-plane loading, $r_ B$ measures the lack of symmetry. Lack of symmetry may produce estrange behavior.

We can either have bending extension coupling:
\includegraphics[]{./Images/Fig67a.png}

or, twisting-extension coupling:
\includegraphics[]{./Images/Fig67c.png}

The latter is significant for a $[55/-55]$ laminate because the laminate is unsymmetric. None of this would occur in a (perfect) orthotropic material.

For bending load we use $r_ B$ (previously defined) and $r_ M$. The latter measures the amount of bending-twisting coupling. A value of zero is ideal. See the textbook for the exact definition of these indicators. The definition for in-plane moduli and bending moduli are displayed on their respective pages in CADEC.